If position vectors of A, B, C, D are respectively \vec{2i}+\vec{3j}+\vec{5k}, \vec{i}+\vec{2j}+\vec{3k}, -\vec{5i}+\vec{4j}-\vec{2k} and \vec{i}+\vec{10j}+\vec{10k}, then

  • Option 1)

    AB\parallel CD

  • Option 2)

    DC\parallel AD

  • Option 3)

    A,B,C are collinear

  • Option 4)

    B,C,D are collinear

 

Answers (1)

As we learnt

Position vector -

Let O be a fixed origin, then position vector of P is \overrightarrow{OP}

- wherein

 

 Since \underset{AB}{\rightarrow}=\left ( p.v \right )\vec{B}-\left ( p.v \right )\vec{A}

So that \underset{AB}{\rightarrow}=\left ( i+2j+3k \right )-\left ( 2i=3j+5k \right )

= -i-j-2k

Similarly \underset{CD}{\rightarrow}=6i+6j+12k

= 6\left ( i+j+2k \right )

So that ratios are equal. so they are parellal

\underset{AB}{\rightarrow}\left | \right |\underset{CD}{\rightarrow}


Option 1)

AB\parallel CD

Correct option

Option 2)

DC\parallel AD

Incorrect Option

Option 3)

A,B,C are collinear

Incorrect Option

Option 4)

B,C,D are collinear

Incorrect Option

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